X-ray diffraction apparatus

ABSTRACT

An X-ray diffraction apparatus comprising means for rotating a specimen in the path of an X-ray beam and means for rotating a diffraction slit simultaneously with the specimen but at a lower angular velocity, so that the X-ray irradiated portion of the specimen remains substantially constant in size during such rotation.

United States Patent 1191 Paolini 1111 3,852,594 1451 Dec. 3, 19m

[ X-RAY DIFFRACTION APPARATUS [75] Inventor: Frank Rudolph Paolini,Stamford,

Conn.

[73] Assignee: Pepi Inc., New York, NY.

[22] Filed: July 25, 1973 21 Appl. No.1 382,481

[52] US. Cl 250/278, 250/273, 250/272 [51] Int. Cl. GOln 23/00 [58]Field of Search 250/277, 278, 491, 279,

[56] References Cited UNITED STATES PATENTS 1/1959 Neff 250/278 7/1961DeLong et a1. 250/505 3/1964 Zingaro 250/278 3,361,909 1/1968 Talas250/278 3,411,000 11/1968 Schliephake et al 250/278 3,566,111 2/1971Harm 250/278 Primary ExaminerArchie R. Borchelt Assistant Examiner-B. C.Anderson Attorney, Agent, or Firm-Frank R. Trifari [57] ABSTRACT AnX-ray diffraction apparatus comprising means for rotating a specimen inthe path of an X-ray beam and means for rotating a diffraction slitsimultaneously with the specimen but at a lower angular velocity, so

- that the X-ray irradiated portion of the specimen re mainssubstantially constant in size during such rotatlOl'l. 7

7 Claims, 5 Drawing Figures LENGTH IRRADIATED 8 (mm) PATENTEL C sure-rear 2 lo Q 0 IO 20 so 40 5 6O 7O 8O ANGLE OF INCIDENCE 9 (deg) X-RAYDIFFRACTION APPARATUS BACKGROUND OF THE INVENTION X-ray diffraction, thedivergence slit serving to form an X-ray beam having desired geometriccharacteristics. During X-ray diffraction analysis the specimen beinginvestigated is rotated about an axis lying in its upper flat surface,to cause the X-raybeam to impinge upon the specimen at various angles,the rotation being so that the angle (0) between the specimen surfaceand a line drawn from the X-ray source to the center of the irradiatedportion thereof ranges between 0 and 90.

During such X-ray diffraction analysis the divergence slit remainsstationary, so that, because of the rotation of the specimen withrespect to the divergence slit and as a result of geometricconsiderations, the area of the specimen irradiated by the X-ray beamvaries between a relatively small amount when the value of 6 is high (e.g 80) and arelatively large amount when the value of 6 is low (e.g.,l0). Such variation of the irradiate area is highly undesirable becauseof numerous adverse effects on the accuracy and reliability of theanalysis.

To cope with such variation of the irradiated area, the prior art hasresorted to using, during each diffraction analysis, stationarydivergence slits of various fixed sizes, with larger slit openings beingemployed for large 0 values and smaller slit openings being employed forsmaller 6 values, thereby tending toequalize the irradiated area of thespecimen as it is rotated over the range of 6 values. Such a practice isundesirable because interchanging the divergence slits is 'atime-consuming process and because it is necessaryto have available anumber of such divergence slits of various sizes, which can be anexpensive proposition, and even more impor tant, because interchaningthedivergence slits still results in a significant amount of variationinthe X-ray irradiated of the specimen.

While the prior art has proposed various method for controlling theirradiated specimen area (see, for example, M. Loisel, Bulletin de laSociete Francaise de Ceramique," Issue No. 90, Jan. March 1971, pp. 55et seq.) such have not been fully desirable nor useful, by reason of,inter alia, their operating on a gross scale that is insufficientlyprecise for the very important small angular values (9) of specimenorientation.

The present invention overcomes, the above shortcomings by providing anapparatus permitting the rotation of the divergence slit in conjuctionwith the rotation of the X-ray irradiated specimen, whereby thedimensions of the X-ray irradiated portion of the specimen remainsubstantially constant during the rotation of the specimen. In apreferred embodiment, the divergence slit is connected to astructural'element linked with a second structural element connected tothe specimen such that the divergence slit rotates at a lower angularspeed than the specimen such that the X-radiation is cut off from thespecimen when the 0 value reaches zero.

DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic representation of aprior art X-ray diffraction apparatus. 7

FIG. 2 is an isometric view of the X-ray diffraction apparatus ofthepresent invention.

FIG. 3 is a schematic representation depicting a feature of the presentinvention.

FIG. 4 is a fragmentary sectional elevation view of a diffraction slitof the type employed in the present invention.

FIG. 5 is a number of curves depicting results obtained with the presentinvention.

THE PREFERRED EMBODIMENT FIG. 1 depicts the situation in the prior artwhere the X-ray diffraction specimen 10 is rotated with respect to astationary divergencejslit 11 through which there passes X-radiation 12from a source 13. When the specimen 10 is acutely disposed (i.e., 0,, isless than to an imaginary line 14 extending between the X-ray source andthe center of the irradiated portion of the specimen, the portion of thespecimen impinged by the X-radiation has a dimension S whereas theimpinged portion dimension S .when when 0,, equals 90 (shown in brokenlines) is substantially less than S Such deviations in the dimensions ofthe X-radiation impinged portion of the specimen are unsatisfactory, asmentioned above.

FIG. 2 depicts a portion of the X-ray diffraction apparatus 20 inaccordance with the present invention, containing and X-ray line source22, as so-called Soller slit assembly 24, a rotatable divergence slit 25mounted via a shaft to a cog wheel 26, a specimen holder 27 connected toa second cog wheel 28, the X-ray diffraction analysis specimen 29 whichis mounted on the holder 27, the second cog wheel 28 being driven by'adrive shaft 30 whose rotatio'ii speed is co-ordinated with the rotationspeed of the goiiiometer'(not shown) used with the diffractionapparatus, a mechanical linking means 31 (i.e., cog belt) linking the'cog wheels 26 and 28, and a receiving slit 32, a Soller slit 33 and ananti-scatter slit 34 all (i.e., 32, 33, and 34) located between thespecimen and the detector 35. It is essential that the divergenceslit'cog wheel 26 include a number of teeth greater than that of thespecimen cog wheel 28 (i.e., a slit cog to specimen cog tooth ratiogreater than 1) so that the former rotates at a lower angular speed(i.e., provides a smaller corresponding angular displacement) than theformer, it being especially preferred that the tooth ratios of these cogwheels be adjusted such that the beam be cut off from the specimen uponthe 6 value reaching zero degrees and that the slit plane and theirradiated specimen surface be substantially parallel when 6 is 90.

By way of the explanation, reference is made to FIG.

. 3 where there are depicted the divergence slit cog where is theangular displacement of the specimen cog wheel 28 and 6,, is the initialangular displacement of the slit cog wheel 26 with respect to specimencog wheel 28 (i.e., the initial angular disposition of the slit withrespect to the specimen irradiated surface). By virtue of thediffraction slits having a finite thickness, the beam is cut off fromthe specimen before 6 reaches zero, so that the geometry ofthediffraction slit should be considered in order that X-ray beamextinction occur (i.e., the beam is cut off from the specimen), underoptimal conditions, when 6 equals exactly 0. Therefore, assuming adiffraction slit having substantially the geometry shown in FIG. 4,wherein r represents the radius ofjthe cylindrical slit-defining portion40 defining the slit opening 42, w represents the width of the opening42 and t represents the thickness of the slit-defining body 43. Whilethe slit is shown with cylinefining portions, other geometries can berectangular slit-definingportions. An imaginary line from and tangent toone face 44 of the slitdefining portion 40, to and tangent to theopposite such face 46 forms an angle, c, with the slitdefining body 43.Therefore, the following expressions can be derived. Where q theextinction, or beam cut off, angle, e, can be deter- 1 mined by thefollowing expressions:

sin e r/k so that e sin (r/k) q- Optimally, X-ray beam extinction occursexactly when 6 0,50 that it is preferred that 0 e at 0= 0. Substitiutingthese conditions into Equation 2 under this optim'al condition resultsin the expression:

i if 0,, isgreater-than e, the length (S) of the X-ray irradiatedportion of the specimen increases rapidly as 6 approaches zero. whereasa value of 6 less than 6 results in a decrease of the irradiated portionlengths as 6 approaches zero. The latter situation (i.e., 9 e) resultsin premature extinction. in that the irradiated portion length is zeroat some 0 value greater than zero. Y it is further optimal that 0' 90when 0 90, so that there is achieved an irradiated specimen portion of.maximum length for values of 6 approaching 90.

Re-writing Equation 4 to satisfy this second optimal condition 0, 90 N/N(90) e Equation 6 establishes the condition that must be met by numbersN and N of cog wheel teeth. N and N must also, of course, be integers.In practice, one picks values that most'closely satisfy Equation 6.

EXAMPLE 1 Using a diffraction slit having a cylindrical slitdefiningbody with a radius r of 0.60 mm, a body thickness t of 1.20 mm, and aslit opening width w of 5.00 mm, the value k of the diffraction slit is3.10 mm and the extinctionan gle, e, is determined from Equation 3 to be11 l0.-Therefore, when 6 0, 0,, should optimally be 11 l0 and, as asecond optimal condition, when 6 90, 6 should also be 90. From Equation6, the cog tooth number ratio, N/N' for the specimen and slit cog wheelsshould be about 79:90 for maintaining an irradiated specimen portion ofsubstantially constant dimensions, this being done automatically duringthe specimen rotation. i I

Using the values 6,, ll0 feet and an NrN' tooth number ratio of 79:90and assuming a distance of 172.00 mm, between the center of theirradiated specimen portion and the X-ray source and a distance of 72.00mm between the X-ray source and the slit center, the length, S, of theirradiated portion of the specimen was calculated for 0 valves over therange of 0 to the resulting S values being shown as Curve l in FIG. 5.In this situation 0 equals 90 when 6 is 90.

.With these same values, except for 0,, 1 1 10 feet,

the length S of the irradiated portion of the specimen was calculatedfor 0 values over the range of 0 to 90, the resulting S values beingshown by Curve ll in FIG. 5. The significant improvement provided bysetting 0,, at exactly the value of e is seen from the comparison ofthese curves, the length, S, of the irradiated portion in Curve ll notexhibiting the relatively sharp drop for the S value for very low 6values i.e., about 6 5. With these same values, except for 6,, and atooth ratio N:N of 90:90 for the slit and specimen cog wheels, the Svalue was calculated over the range of 6 0 to- 0 90, the results beingdepicted as Curve ill in FIG. 5. The significant improvement provided bythe present invention is seen-from the comparison of these Curves, thelength, S, of the irradiated portion remaining substantially'constantover substantially all'of the range between 6 Oto 0 90 (Curves land ll)when the slit cog: specimen cog tooth ratio is greater than 1 (i.e.,90:79), whereas, as shown by Curve Ill, the length, S drops dramaticallyfor 0 values below about 0 50 and is zero at about 8 12 for thesituation where the cog wheels have the same number of teeth (i.e. N N).

Thus, the present invention permits achieving an irradiated specimenportion of substantially constant dimensions over the rotation range foranalyzed specimen. While setting 0,, at exactly eleads to a deviation of0 from 90 when 6 equals 90, it is felt to be more preferable to set 6.,at exactly the value of the extinction angle,,e, notwithstanding thefact that 6' will not equal 6 at 6 90, in order to avoid the drop in Svalues about 0 equals 5 and less.

- lclaim:

1. An X-ray diffraction apparatus comprising:

a. a source of X-rays;

b. means for holding an X-ray diffraction specimen in the path of saidX-ray beam such that a portion of said specimen can be impinged by saidbeam;

c. means for rotating said specimen at a first angular velocity from afirst position to a second position;

cl. a diffraction slit disposed between said specimen and said sourcesuch that said X-rays pass throug the opening of said slit;

e. means for rotating said diffraction slit simultaneously with thespecimen, said difiraction slit being so rotated at a second angularvelocity lower than said first angular velocity; and

f. means for measuring the intensity of X-rays reflected from saidspecimen, whereby said irradiated portion remains substantially constantthroughout the rotation of said specimen.

2. An'X-ray diffraction apparatus as defined in claim 1, wherein at saidfirst position said position is substantially perpendicular to animaginary line extending from said X-ray source to the center of saidportion and said second position said portion is substantially parallelto said imaginary lines and said diffraction slit is rotated betweenthird and fourth positions, said diffraction on slit at said thirdposition being substantially parallel to said specimen at said thirdposition being substantially parallel to said specimen at said firstposition and at said fourth position being obliquely disposed to saidspecimen at said second position.

3. An X-ray diffraction appparatus as defined in claim 1, wherein saidmeans for rotating said specimen comprises a first cog wheel and saidmeans for rotating said diffraction slit comprises a second cog wheeldriven by said first cog wheel. 7

4. An X-ray diffraction apparatus as defined in claim 3, wherein thegear ratio of said first cog wheel to said second gear wheel is lessthan one.

5. An X-ray diffraction apparatus as defined in claim 4, wherein saidfirst gear wheel is mechanically linked to and drives said second gearwheel.

6. An X-ray diffraction apparatus as defined in claim 3, wherein theangular displacement 6' of said second gear wheel is determinable fromthe expression:

where N and N are the teeth numbers for said first and second gearwheels, respectively;

0 is the angular displacement of said first gear wheel;

and 1 e is the angular orientation of said second gear wheel when saidbeam iscut off from said specimen located at said second position.

7. A method of operating an X-ray diffraction apparatus comprising thesteps of: r

a. providing an X-ray beam source;

b. providing an X-ray diffraction specimen disposed at an angle ofsubstantially zero degrees with respect to said X-ray beam;

c. providing an X-ray diffraction slit between the source of said beamand said specimen, said diffraction slit being disposed at substantiallythe extinction angle thereof when said specimen is disposed at 0 withrespect to said beam, said specimen being rotatable over a range of saidangles of from zero to about 90 and said slit being rotatable I at alower angular velocity than said specimen and over an angular rangeextending from said extinction angle to about 90;

d. irradiating said specimen with said X-ray beam and simultaneouslyrotating said specimen and said slit over said ranges of angles; and

e. measuring the intensity of X-rays reflected from said specimen.

1. An X-ray diffraction apparatus comprising: a. a source of X-rays; b.means for holding an X-ray diffraction specimen in the path of saidX-ray beam such that a portion of said specimen can be impinged by saidbeam; c. means for rotating said specimen at a first angular velocityfrom a first position to a second position; d. a diffraction slitdisposed between said specimen and said source such that said X-rayspass through the opening of said slit; e. means for rotating saiddiffraction slit simultaneously with the specimen, said diffraction slitbeing so rotated at a second angular velocity lower than said firstangular velocity; and f. means for measuring the intensity of X-raysreflected from said specimen, whereby said irradiated portion remainssubstantially constant throughout the rotation of said specimen.
 2. AnX-ray diffraction apparatus as defined in claim 1, wherein at said firstposition said position is substantially perpendicular to an imaginaryline extending from said X-ray source to the center of said portion andsaid second position said portion is substantially parallel to saidimaginary lines and said diffraction slit is rotated between third andfourth positions, said diffraction on slit at said third position beingsubstantially parallel to said specimen at said third position beingsubstantially parallel to said specimen at said first position and atsaid fourth position being obliquely disposed to said specimen at saidsecond position.
 3. An X-ray diffraction appparatus as defined in claim1, wherein said means for rotating said specimen comprises a first cogwheel and said means for rotating said diffraction slit comprises asecond cog wheel driven by said first cog wheel.
 4. An X-ray diffractionapparatus as defined in claim 3, wherein the gear ratio of said firstcog wheel to said second gear wheel is less than one.
 5. An X-raydiffraction apparatus as defined in claim 4, wherein said first gearwheel is mechanically linked to and drives said second gear wheel.
 6. AnX-ray diffraction apparatus as defined in claim 3, wherein the angulardisplacement theta '' of said second gear wheel is determinable from theexpression: theta '' N/N'' theta + epsilon , where N and N'' are theteeth numbers for said first and second gear wheels, respectively; thetais the angular displacement of said first gear wheel; and epsilon is theangular orientation of said second gear wheel when said beam is cut offfrom said specimen located at said second position.
 7. A method ofoperating an X-ray diffraction apparatus comprising the steps of: a.providing an X-ray beam source; b. providing an X-ray diffractionspecimen disposed at an angle of substantially zero degrees with respectto said X-ray beam; c. providing an X-ray diffraction slit between thesource of said beam and said specimen, said diffraction slit beingdisposed at substantially the extinction angle thereof when saidspecimen is disposed at 0* with respect to said beam, said specimenbeing rotatable over a range of said angles of from zero to about 90*and said slit being rotatable at a lower angular velocity than saidspecimen and over an angular range extending from said extinction angleto about 90*; d. irradiating said specimen with said X-ray beam andsimultaneously rotating said specimen and said slit over said ranges ofangles; and e. measuring the intensity of X-rays reflected from saidspecimen.